Let's take a scaled-down version of Hydra's plan.
You work for Hydra, and you believe in it.
The person next to you (we'll call her Colleen) isva potential threat. In fact, based on everything Zoloff's algorithm has been able to deduce, she's not just a potential threat, she is a threat, with a circle on influence that extends far enough to be a concern. Being a member of Hydra, you are not above ignoring her Constitutional rights to quell her influence. In fact, it all comes down to the fact that she should have no Constitutional rights because she should not even be considered a citizen at all. You have no problem with your organization taking her off the streets, questioning her, even resorting to torturing her to get more information.
But Hydra's plan isn't to remove her form the street.... it's more like asking you to take out our gun and shoot her in the head in front of everyone. Only Hydra's plan is much worse, it means doing that to a million people all at once, despite the fact that those million people are all threats.
So even if you agree that any threats should not be given due process, you are still a human being,.. (you are doing this to protect people, and the film even says that Hydra was founded on the idea that humanity could not be trusted with its own freedom) so the Consitution be damned but being hat Hydra is comprised of humans.. humans emathetic enough to at least care about the health of society, it would certainly not be unreasonable to think that many of them would balk (or at least second guess) the notion of violently killing people in broad daylight. Sure you have liek that one din the film.. I forget his name, but the guy that Falcon fights near the end, who would totally not care how these threats are dealt with, but there are going to be those people who believe in Hydra and its goals but who also care. So with Insight's knowledge of human nature, it would have to take that into account...